How many ENSO flavors can we distinguish?* - ? How many ENSO flavors can we distinguish?* Nathaniel

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  • How many ENSO flavors can we distinguish?*

    Nathaniel C. Johnson

    International Pacific Research Center, SOEST, University of Hawaii at Manoa,

    Honolulu, Hawaii

    Journal of Climate

    Revised December 23, 2012

    ____________________ *International Pacific Research Center publication number XXX

    Corresponding author address: Nathaniel Johnson, IPRC, University of Hawaii at Manoa, 401 POST Building,

    Honolulu, HI, 96822.

    E-mail: natj@hawaii.edu

  • 1

    ABSTRACT 1

    2

    It is now widely recognized that the El Nio-Southern Oscillation (ENSO) occurs in 3

    more than one form, with the canonical eastern Pacific (EP) and more recently recognized 4

    central Pacific (CP) ENSO types receiving the most focus. Given that these various ENSO 5

    flavors may contribute to climate variability and long-term trends in unique ways, and that 6

    ENSO variability is not limited to these two types, this study presents a framework that treats 7

    ENSO as a continuum but determines a finite, maximum number of statistically distinguishable 8

    representative ENSO patterns. A neural network-based cluster analysis called self-organizing 9

    map (SOM) analysis paired with a statistical distinguishability test determine nine unique 10

    patterns that characterize the September February tropical Pacific SST anomaly fields for the 11

    period from 1950 through 2011. These nine patterns represent the flavors of ENSO, which 12

    include EP, CP, and mixed ENSO patterns. Over the 1950-2011 period, the most significant 13

    trends reflect changes in La Nia patterns, with a shift in dominance of La Nia-like patterns 14

    with weak or negative west Pacific warm pool SST anomalies until the mid 1970s, followed by a 15

    dominance of La Nia-like patterns with positive west Pacific warm pool SST anomalies, 16

    particularly after the mid 1990s. Both an EP and especially a CP El Nio pattern experienced 17

    positive frequency trends, but these trends are indistinguishable from natural variability. 18

    Overall, changes in frequency within the ENSO continuum contributed to the pattern of tropical 19

    Pacific warming, particularly in the equatorial eastern Pacific and especially in relation to 20

    changes of the La Nia-like rather than El Nio-like patterns. 21

    22

    23

    24

  • 2

    1. Introduction 25

    The El Nio-Southern Oscillation (ENSO) is the dominant mode of tropical atmosphere-26

    ocean interaction on interannual timescales, with impacts that span much of the globe 27

    (Ropelewski and Halpert 1987; Trenberth and Caron 2000). Typically, ENSO episodes have 28

    been identified through the monitoring of sea surface temperature (SST) anomalies in the 29

    equatorial Pacific region, most notably the so-called Nio 3.4 region (5S - 5N, 120 - 170W). 30

    However, recent studies have made it increasingly clear that traditional definitions of ENSO 31

    episodes fail to distinguish two unique types of El Nio episode, the canonical El Nio that is 32

    centered in the eastern equatorial Pacific and the more recently recognized El Nio that is 33

    centered farther west near the International Date Line. This latter type, which has been referred 34

    by various names such as the dateline El Nio (Larkin and Harrison 2005), El Nio Modoki 35

    (Ashok et al. 2007), warm pool El Nio (Kug et al. 2009), and central Pacific El Nio (Yeh 36

    et al. 2009), has received increased attention because of its unique underlying dynamics (Kao 37

    and Yu 2009; Kug et al. 2009; Newman et al. 2011a,b; Yu and Kim 2011), global impacts 38

    (Larkin and Harrison 2005; Weng et al. 2007; Ashok et al. 2007; Mo 2010; Hu et al. 2012), and 39

    potential trends under global warming (Yeh et al. 2009) relative to those of the eastern Pacific 40

    (EP) El Nio. On the basis of climate model simulations analyzed in the IPCC Fourth 41

    Assessment Report, Yeh et al. (2009) suggest that the relative frequency of central Pacific (CP) 42

    El Nio episodes may increase under anthropogenic global warming in response to changes in 43

    the equatorial Pacific mean thermocline. However, the recent increasing trend in the frequency 44

    of CP El Nio episodes (Lee and McPhaden 2010) may be indistinguishable from natural 45

    variability (Newman et al. 2011b; Yeh et al. 2011). 46

  • 3

    The recent focus on the distinction between the EP and CP El Nio is consistent with the 47

    notion that ENSO may come in many different flavors (Trenberth and Stepaniak 2001) that are 48

    distinct from the canonical El Nio and La Nia composites and cannot be characterized by a 49

    single index. In order to describe the structure and evolution of these various flavors, 50

    investigators have increasingly considered multiple indices that capture the zonal gradient of 51

    equatorial Pacific SST anomalies such as the Trans-Nio Index (Trenberth and Stepaniak 52

    2001) or, more commonly for the identification of EP and CP El Nio episodes, a comparison 53

    between Nio 3 (5S - 5N, 150 - 90W) and Nio 4 region (5S - 5N, 160E - 150W) SST 54

    anomalies. Although this additional information clearly reveals some of the distinct properties 55

    between various ENSO episodes, such subjective index choices are not necessarily optimal for 56

    describing the various ENSO flavors that are discernible in the observational record. 57

    Another common approach for distinguishing tropical SST patterns is through empirical 58

    orthogonal function (EOF) analysis, but this method is not guaranteed to reveal physically 59

    interpretable SST modes (e.g., LHeureux et al. 2012). In particular, the leading EOF of tropical 60

    Pacific SSTs generally resembles the canonical EP ENSO pattern, and either the second (e.g., 61

    Ashok et al. 2007) or third (e.g., LHeureux et al. 2012) EOF resembles the CP ENSO pattern. 62

    However, this second or third EOF also tends to capture the spatial asymmetry between the EP 63

    El Nio and La Nia patterns (Hoerling et al. 1997; Rodgers et al. 2004), which means that this 64

    particular EOF is not uniquely identified with CP ENSO episodes. This complication highlights 65

    one of the potential pitfalls of using a linear, orthogonal method like EOF analysis to 66

    characterize nonlinear, non-orthogonal SST patterns. 67

    In this study we consider a new perspective and methodology for describing ENSO 68

    flavors. Under the perspective presented here, we recognize that there is a continuum of ENSO 69

  • 4

    states but that the relatively brief observational record limits the number of distinct ENSO 70

    flavors that we can distinguish. Here we consider a methodology that treats ENSO as a 71

    continuum but also determines a finite, maximum number of statistically distinguishable ENSO 72

    flavors. This approach is based on a pairing of a type of neural network-based cluster analysis, 73

    called self-organizing map (SOM) analysis, with a statistical distinguishability test, described 74

    more thoroughly in the following section. This approach represents a more objective partitioning 75

    of the equatorial Pacific SST data than the standard approach of partitioning by somewhat 76

    subjective SST indices. In addition, this approach, which is constrained by neither linearity nor 77

    orthogonality, avoids the disadvantages of common linear methods such as EOF analysis and 78

    often results in more easily interpretable physical patterns (Reusch et al. 2005; Liu et al. 2006; 79

    Johnson et al. 2008). 80

    Because tropical SST trends play a critical role in remote, regional temperature and 81

    precipitation trends (Shin and Sardeshmukh 2011) and tropical precipitation and circulation 82

    changes (Xie et al. 2010; Johnson and Xie 2010; Ma et al. 2012; Tokinaga et al. 2012), it is 83

    worthwhile to examine how changes in the frequency of different ENSO flavors impact the long-84

    term SST trend. As demonstrated and discussed in the following three sections, the framework 85

    adopted here allows us to connect the long-term SST trend to changes in the frequency 86

    distribution of interannually varying SST patterns. 87

    The remainder of the paper is organized as follows. Section 2 provides a description of 88

    the general framework, methodology, and data used in this analysis. Section 3 presents the main 89

    results, which include the SOM cluster patterns and the results of the trend analysis. The paper 90

    concludes with discussion and conclusions in Sections 4 and 5. 91

    92

  • 5

    2. Data and Methodology 93

    In this section we examine the approach for determining the ENSO region SST clusters 94

    and then determining the maximum number of distinguishable clusters. 95

    96

    a. Self-organizing map SST cluster patterns 97

    98

    Conceptually, we would expect that determining the maximum number of distinguishable 99

    ENSO flavors would require a partitioning of tropical Pacific SST fields into groups that 100

    maximize similarity within groups while also maximizing the dissimilarity between groups. 101

    Computationally, this sort of partitioning may be accomplished either by K-means cluster or 102

    SOM analysis. Specifically, K-means cluster analysis treats each SST field as an M-dimensional 103

    vector, where M is the number of grid points, and minimizes the sum of squared distances 104

    between each SST field and the nearest of the K cluster centroids. There are several reasonable 105

    choices for a distance metric, but Euclidean distance is perhaps most commonly used, and is 106

    used in the analysis presented here. The clusters are most commonly determined through an 107

    iterative, two-step procedure described as such: Given an initial assignment of K cluster 108

    centroids, which may be a random distribution, the first step is the assignment of the data vectors 109

    (SST fields in this case) to the nearest cluster centroid, and the second step is the calculation of 110

    the new cluster centroids. These two steps are repeated until the cluster assignments no longer 111

    change, which corresponds to a local minimum of the sum of squared distances described above. 112

    The value of K must be specified prior to the cluster analysis, and the method for determining K 113

    for this problem is discussed in Section 2b. K-means cluster analysis has remained a popular 114

    method of cluster analysis in the atmospheric and ocean sciences for decades (e.g., Michelangeli 115

  • 6

    et al. 1995; Christiansen 2007; Johnson and Feldstein 2010; Riddle et al. 2012; Freeman et al. 116

    2012). 117

    SOM analysis (Kohonen 2001) is a relatively new neural network-based cluster analysis 118

    that bears strong similarities to K-means clustering and has increased in popularity in the 119

    atmospheric and ocean sciences over the past decade (e.g., Hewitson and Crane 2002; 120

    Richardson et al. 2003; Liu et al. 2006; Leloup et al. 2007; Johnson et al. 2008; Jin et al. 2010; 121

    Lee et al. 2011; Chu et al. 2012). SOM analysis most significantly distinguishes itself from K-122

    means cluster analysis through the addition of a topological ordering on a low-dimensional 123

    (typically one- or two-dimensional) map. In other words, the clusters self-organize such that 124

    similar clusters are located close together on this low-dimensional map, often displayed as a grid, 125

    and dissimilar clusters are located farther apart. This combination of clustering and topological 126

    ordering makes SOM analysis effective for providing a visualization of the continuum of 127

    patterns within a dataset. Similar to the objectives of this study, SOM analysis has been used in 128

    previous studies to describe the continuum of atmospheric teleconnection patterns (e.g., Johnson 129

    et al. 2008; Lee et al. 2011) and to describe decadal changes in ENSO (Leloup et al. 2007). 130

    The self-organizing nature of SOM analysis owes to a component called the 131

    neighborhood function, with an associated parameter called the neighborhood radius. When the 132

    neighborhood radius is greater than zero, the clusters become organized within the low-133

    dimensional map. When the neighborhood radius is set to zero, the SOM algorithm reduces to 134

    the K-means clustering algorithm. Thus, SOM analysis can be considered a constrained version 135

    of K-means clustering (Hastie et al. 2009). In the present analysis, a one-dimensional SOM 136

    analysis is performed such that the neighborhood radius gradually shrinks to a value of zero. 137

    Therefore, the SOM patterns become topologically ordered along a line when the neighborhood 138

  • 7

    radius is greater than zero, but the algorithm used to determine the cluster patterns converges to 139

    the K-means clustering algorithm. The SOM approach is chosen to ensure that similar ENSO 140

    flavors are grouped together, but we would expect to see similar results with K-means cluster 141

    analysis. See the appendix of Johnson et al. (2008) for a more thorough description of the basic 142

    SOM methodology and Liu et al. (2006) for additional information on recommended SOM 143

    parameter choices. 144

    In this study, we consider ENSO flavors to be represented by SOM SST anomaly patterns 145

    in the equatorial Pacific domain. We use September February mean SST data for the period 146

    from 1950 through 2011 derived from the Extended Reconstructed Sea Surface Temperature 147

    Dataset, Version 3b (ERSST v3b; Xue et al. 2003; Smith et al. 2008). The September 148

    February period is used because of the seasonal phase locking of ENSO, which results in the vast 149

    majority of ENSO episodes peaking during boreal fall or winter. The starting year of 1950 is 150

    chosen because of the improved spatial and temporal coverage of SST data that begins around 151

    that time (Deser et al. 2010; see their Fig. 3). In addition, prior to 1950 the SST patterns of 152

    ENSO episodes may depend strongly on the method of reconstruction for the SST dataset (Giese 153

    and Ray 2011; Ray and Giese 2012). The chosen domain covers the tropical Pacific region 154

    between 120E and 50W and between 25S and 25N. The ERSST v3b data are on a 2 155

    latitude-longitude grid, but because the analysis described in the following section requires equal 156

    weight to be placed on each grid point, the data are linearly interpolated to an equal-area grid 157

    with 1 latitudinal spacing and longitudinal spacing that increases from 1 at the equator to 158

    approximately 1.1 at 25 latitude. Anomalies are calculated by subtracting the seasonal cycle 159

    for the 1981-2010 base period. The choice of the most recent 30-year climatology is based on 160

    the standard practice of the National Oceanic and Atmospheric Administration (NOAA) Climate 161

  • 8

    Prediction Center (CPC), but the focus of this study, the spatial variations and trends of ENSO 162

    flavors, is not sensitive to this choice of base period. SOM analysis is performed on the SST 163

    anomaly data for various choices of K, as described in section 2b. Because the analysis 164

    converges to a local rather than global minimum of the error function described at the beginning 165

    of this section, the SOM analyses and all tests of Section 2b are repeated five times without any 166

    noticeable change in results. Thus, the results presented here are robust. All SOM calculations 167

    are performed with the Matlab SOM Toolbox (Vesanto et al. 2000) that is freely available on the 168

    Web (http://www.cis.hut.fi/somtoolbox/). 169

    170

    b. Determining the maximum number of distinguishable ENSO flavors 171

    172

    Because K must be specified prior to a K-means cluster or SOM analysis, one challenge 173

    in any cluster analysis is the determination of the optimal number of clusters. Many studies have 174

    suggested various useful heuristic methods for determining K (e.g., Michelangeli et al. 1995; 175

    Christiansen 2007; Hastie et al. 2009; Riddle et al. 2012), but an objective optimal K has 176

    remained elusive. In this study we consider a new criterion for choosing K: the maximum 177

    number such that all clusters are statistically distinguishable from another. Thus, if K* is the 178

    optimal K by this criterion, then we can determine K* unique cluster patterns, but K*+1 clusters 179

    would result in two or more clusters that are indistinguishable by this statistical definition. In the 180

    present application, K* would refer to the maximum number of statistically discernible ENSO 181

    flavors. 182

    The determination of whether two cluster patterns are statistically distinguishable 183

    requires a test of field significance. Often times in the atmospheric and ocean sciences, field 184

  • 9

    significance tests have been conducted through Monte Carlo resampling methods (Livezey and 185

    Chen 1983). Recently, another field significance approach based on the false discovery rate 186

    (FDR) has been introduced to the climate sciences (Benjamini and Hochberg 1995; Wilks 2006). 187

    The FDR refers to the expected proportion of local null hypotheses that are rejected but are 188

    actually true. In the present application, the local hypotheses being evaluated are whether the 189

    SST anomalies at each grid point in cluster pattern i are significantly different from the 190

    corresponding SST anomalies in cluster pattern j. If at least one local test has a p-value that 191

    satisfies the specified FDR criterion, typically q = 0.05, then the cluster patterns are statistically 192

    distinguishable also at the level q. If no local tests meet the FDR criterion, then the cluster 193

    patterns are statistically indistinguishable. Further explanation of this test is provided below. 194

    The FDR approach has a number of advantages over conventional field significance tests, 195

    including generally better test power, robust results even when the local test results are correlated 196

    with each other, and the identification of significant local tests while controlling the proportion 197

    of false rejections (Wilks 2006). In addition, FDR tests are much more computationally efficient 198

    than Monte Carlo methods, and so a large number of field significance tests can be conducted 199

    with little computational effort, as required for the tests described here. 200

    To determine if SOM cluster i is statistically distinguishable from SOM cluster j, we first 201

    calculate the p-values (two-sided) at each grid point corresponding to the Students t distribution 202

    for a difference of means, where the null hypothesis is that the local SST composite anomalies 203

    are the same in both clusters. This test is based on the recognition that SOM cluster pattern i (j) 204

    with ni (nj) cluster members is equivalent to an SST composite pattern with ni (nj) samples that 205

  • 10

    comprise the composite1. Each of the ni or nj cluster members is a seasonal SST anomaly field 206

    assigned to that cluster on the basis of minimum Euclidean distance. For each pair of cluster 207

    pattern composites, we calculate the p-values corresponding to 208

    t(,) =

    (1) 209

    where 210

    S( ) =

    (2) 211

    The variable ( ) signifies the composite SST anomaly for SOM cluster i (j), and Si (Sj) 212

    indicates the standard deviation corresponding to all SST anomalies within cluster i (j) at latitude 213

    and longitude . For these calculations, we assume that each SST anomaly field represents an 214

    independent sample, which is reasonable for seasonal fields separated by at least a year and 215

    usually several years within each cluster. 216

    The calculations for a pair of cluster patterns described above result in a distribution of M 217

    p-values, where, again, M is the total number of grid points. If all M local null hypotheses are 218

    true, and if the results of the local tests are independent of each other, then the resulting M p-219

    values will be a random sample from the uniform distribution U(0,1) (e.g., Folland and Anderson 220

    2002; Wilks 2006). If some of the local null hypotheses are false, then the corresponding p-221

    values will be smaller than expected from this uniform distribution. The FDR test evaluates the 222

    distribution of p-values to determine the local p-value that provides confidence in the correct 223

    rejection of local null hypotheses; that is, the p-value that controls the FDR at the level q, which 224

    1 The equivalence between SOM cluster patterns and composites is strictly true only when the neighborhood radius

    of the SOM algorithm is equal to zero, as specified as the final radius in this analysis. This equivalence is always

    true for K-means cluster analysis.

  • 11

    is also the global or field significance level global. This test is conducted as follows. Let p(m) 225

    denote the mth smallest of the M p-values. The FDR can be controlled at the level q for 226

    . (3) 227

    All local tests that yield a p-value less than or equal to the largest p-value that satisfies the right-228

    hand side of (3) are deemed significant, which means that the expected fraction of local null 229

    hypotheses that are actually true for those tests is less than or equal to q. If no local tests meet 230

    the criterion specified in (3), then the patterns are statistically indistinguishable. In the present 231

    application, we shall not focus on the specific value of pFDR, but instead shall focus on whether 232

    or not any local tests satisfy (3) for q = 0.05; that is, whether or not the cluster patterns are 233

    statistically distinguishable at the 95% confidence level. Although the assumption of 234

    independent local tests does not hold in this case due to high spatial correlation in the SST fields, 235

    the results of FDR tests do not appear sensitive to this independence assumption (Wilks 2006). 236

    For K SOM cluster patterns there are K(K-1)/2 possible pairs of patterns to compare with 237

    the test described above. To determine K*, we perform the SOM analysis for values of K that 238

    increase from two to 20 at an increment of one, perform the K(K-1)/2 field significance tests, as 239

    described above, for each choice of K, and count the number of SOM cluster pattern pairs that 240

    are statistically indistinguishable. The maximum number of statistically distinguishable ENSO 241

    flavors, K*, is the largest value of K with zero statistically indistinguishable cluster pattern pairs. 242

    243

    3. Results 244

    We first examine the results of the field significance tests described above. Figure 1 245

    illustrates the number of statistically indistinguishable cluster pattern pairs as a function of K. 246

  • 12

    We see that as K is increased from two to nine, all pairs of cluster patterns for each K remain 247

    statistically distinguishable. When K is increased to ten, however, the number of statistically 248

    indistinguishable pairs rises above zero. As we would expect, the number of indistinguishable 249

    pairs rises monotonically with K above nine2. Thus, by the reasoning stated above, the 250

    maximum number of statistically distinguishable ENSO flavors is determined to be nine. 251

    The value of K* may vary slightly based on the domain chosen to represent ENSO 252

    flavors. Reasons for the slight variations include changes in the number of spatial degrees of 253

    freedom, the convergence of cluster analyses to local rather than global minima of the error 254

    functions, and the use of a sharp significance threshold of global = 0.05. However, we do obtain 255

    the same value of K* when we change the northern and southern boundaries to 20N/S or move 256

    the western boundary to 90E. Moreover, the analysis performed on both smaller and larger 257

    domains results in similar interpretations of the variability and trends, supporting the robustness 258

    of the results discussed below. 259

    260

    a. SOM of tropical Pacific SST patterns 261

    262

    With K* determined, we now examine the nine SOM cluster patterns of tropical Pacific 263

    SST anomalies. Figure 2 presents these nine patterns for the one-dimensional SOM. Because of 264

    the topological ordering by the SOM, similar patterns are similarly numbered. Figure 2 reveals 265

    three moderate to strong La Nia-like patterns (patterns 1-3), two weak La Nia-like patterns 266

    (patterns 4-5), two weak CP El Nio-like patterns (patterns 6-7), a moderate CP/EP El Nio-like 267

    pattern (pattern 8) and a strong EP El Nio-like pattern (pattern 9). In addition to amplitude, the 268

    2 If a SOM cluster has only a single member, then (1) is undefined, and the distinguishability test cannot be

    conducted. Therefore, in cases where a cluster only has one member, all pairs that include that particular cluster are

    automatically assigned as statistically indistinguishable.

  • 13

    La Nia-like patterns most significantly distinguish themselves by the longitude of maximum 269

    equatorial cooling and by the presence of weak (pattern 1), negative (patterns 2 and 5), or 270

    positive (patterns 3 and 4) western Pacific SST anomalies. The El Nio-like patterns also 271

    distinguish themselves by amplitude and the longitude of maximum equatorial SST anomalies, 272

    but the western Pacific SST anomalies are similar for each El Nio-like pattern. Pattern 9 273

    resembles the canonical EP El Nio, whereas pattern 8 seemingly represents a hybrid EP/CP El 274

    Nio pattern, with maximum warming in the central Pacific, but a tongue of positive SST 275

    anomalies that extends to the South American coast. Together, these nine SST patterns represent 276

    the ENSO SST continuum. 277

    As mentioned above, each September February SST field is assigned to the best-278

    matching SOM pattern on the basis of minimum Euclidean distance. The frequency of 279

    occurrence of each SOM pattern is indicated to the bottom right of each map, revealing that most 280

    patterns occur with similar frequency. To verify that these nine patterns do, in fact, resemble the 281

    seasonal SST fields that comprise the clusters, centered pattern correlations (e.g., Santer et al. 282

    1993) between each SST field and its corresponding best-matching SOM pattern are calculated. 283

    The mean pattern correlation is 0.76, which confirms the close resemblance between these nine 284

    patterns and the individual constituent SST anomaly fields of each cluster. 285

    286

    b. Changes in frequency distribution within the ENSO continuum 287

    288

    Next we examine how the frequency of occurrence of these nine SOM patterns has varied 289

    over the past 60 years and how these changes in frequency have influenced the long-term 290

    tropical Pacific SST trends. Figure 3 illustrates the occurrence time series for each of the nine 291

  • 14

    patterns. This plot demonstrates that each SOM pattern generally occurs for a single season and 292

    for no more than two consecutive years. In addition, Figure 3 indicates whether at least four of 293

    the six months in the September through February season are classified as an El Nio or La Nia 294

    episode by NOAA CPC. NOAA CPC classifies an El Nio (La Nia) episode when the three-295

    month running mean Nio 3.4 SST anomaly is greater than 0.5C (less than -0.5C) for at least 296

    five consecutive overlapping, three-month seasons. Figure 3 confirms that patterns 1-4 are 297

    closely associated with La Nia episodes, and patterns 6-9 are tied to El Nio episodes. Pattern 298

    5 generally occurs when neutral ENSO conditions are declared. The CP El Nio episodes noted 299

    in previous literature (e.g., Kug et al. 2009) generally correspond with SOM patterns 6 (e.g, 300

    1977/78 and 1990/91), 7 (e.g., 2004/05), or 8 (e.g., 1994/95 and 2002/03). The only clearly 301

    defined EP El Nio pattern, SOM pattern 9, corresponds with the strong El Nio episodes of 302

    1972/73, 1982/83, and 1997/98. This observation that recent strong El Nio episodes have 303

    strongly positive SST anomalies centered in the eastern Pacific, but that all other El Nio 304

    episodes are centered over a broad range of longitudes is consistent with the recent studies of 305

    Giese and Ray (2011) and Ray and Giese (2012). 306

    Perhaps the most striking feature of Fig. 3 is the obvious trend in patterns 1-4, with 307

    patterns 1 and 2 prevalent early in the period but nearly absent in the second half of the period, 308

    and patterns 3 and 4 prevalent only after the mid 1990s. This trend represents a transition from 309

    La Nia-like patterns with weak or negative SST anomalies in the western Pacific warm pool 310

    (patterns 1 and 2) to La Nia-like patterns with positive SST anomalies in the western Pacific 311

    warm pool (patterns 3 and 4). 312

    This transition is demonstrated more clearly in Figure 4, which shows the trend in the 313

    frequency of occurrence for each SOM pattern. Statistical significance is assessed with respect 314

  • 15

    to a K-state first-order Markov chain, as determined through a Monte Carlo test similar to that of 315

    Riddle et al. (2012). For this test, 10,000 synthetic first-order Markov chain SOM pattern 316

    occurrence time series (like that of Fig. 3) are generated with the same transition probabilities as 317

    observed. For each synthetic time series the trend in pattern frequency of occurrence is 318

    calculated. Observed trends that are greater than the 97.5th

    or less than the 2.5th

    percentile of the 319

    synthetic trends are deemed statistically significant above the 95% confidence level. Figure 4 320

    confirms that the trends in SOM patterns 1-4 are strongest, with only the trend in pattern 3 falling 321

    just short of statistical significance. Although flavors of El Nio have received more focus than 322

    those of La Nia, none of the trends in the El Nio-like patterns (patterns 6-9) is statistically 323

    significant over the past 60 years. 324

    To determine how these SOM pattern frequency trends have contributed to the total 325

    tropical Pacific SST trends, we calculate the SOM-derived trend as 326

    (4) 327

    where

    is the frequency trend of SOM pattern i, and SSTi is SOM pattern i. Figure 5 presents 328

    the total and SOM-derived September February SST trends over the tropical Pacific region. 329

    The total SST trend (Fig. 5a) reveals warming over the past 60 years over almost the entire 330

    domain, but the most pronounced warming is indicated over the eastern equatorial Pacific and 331

    western Pacific warm pool. The trend derived from (4) (Fig. 5b) also shows warming over most 332

    of the domain, but the warming is most pronounced only over the eastern Pacific region. Figure 333

    4 suggests that most of these ENSO flavor-related trends relate to changes in the frequency of La 334

    Nia-like rather than El Nio-like patterns. This suggestion is confirmed in Fig. 6, which shows 335

    the trends from the application of (4) only for La Nia-like SOM patterns 1-5 (Fig. 6a) and only 336

    for El Nio-like SOM patterns 6-9 (Fig. 6b). The trend pattern derived solely from La Nia-like 337

  • 16

    pattern frequency changes (Fig. 6a) closely resembles the total ENSO-related trend pattern (Fig. 338

    5b). The positive trends in El Nio-like pattern frequencies have contributed to modest warming 339

    in the eastern equatorial Pacific region, but El Nio-related trends are weak throughout the rest 340

    of the domain (Fig. 6b). 341

    The difference between the total and SOM-derived trends (Fig. 5c) reveals generally 342

    weak and even negative SST trends over the equatorial Pacific domain but with pronounced 343

    positive trends remaining over the west Pacific warm pool. This result suggests that trends in the 344

    frequency of occurrence of various ENSO flavors have dominated the SST trends in the eastern 345

    equatorial Pacific region, but the trends in the west Pacific warm pool reflect a combination of 346

    changes in frequency distribution and an additional superimposed long-term non-ENSO trend. 347

    348

    4. Discussion 349

    The preceding analysis reveals nine statistically distinguishable patterns that represent the 350

    ENSO continuum. This continuum perspective contrasts the framework of recent studies that 351

    suggest two clearly distinct types of El Nio. This continuum perspective also is supported by 352

    the recent work of Giese and Ray (2011), who find that the central longitude of El Nio SST 353

    anomalies is not bimodal but rather is indistinguishable from a Gaussian distribution centered 354

    near 140W. One notable observation is that the three strongest El Nio episodes of the past 60 355

    years as measured by Nio 3.4 SST anomalies (1972/73, 1982/83, and 1997/98) feature strongest 356

    SST anomalies in the eastern Pacific (SOM pattern 9). Perhaps the increased attention paid to 357

    these strongest episodes has resulted in an over-emphasized sharpening of the differences 358

    between EP and CP El Nio episodes. Evidence from an ocean reanalysis suggests that these 359

    strong EP El Nio episodes may have resulted in an eastward bias of reconstructed El Nio SST 360

  • 17

    anomalies for periods before 1950 owing to the influence of these strong El Nio episodes on the 361

    SST reconstructions (Giese and Ray 2011; Ray and Giese 2012). 362

    The analysis also reveals that these nine ENSO flavors have made a significant 363

    contribution to the long-term tropical Pacific SST trend through changes in their frequency 364

    distribution (Fig. 5b). The most significant trends relate to the La Nia-like patterns, with the 365

    dominance of patterns with negative western Pacific SST anomalies (patterns 1 and 2) before the 366

    mid 1970s followed by the dominance of patterns with positive western Pacific SST anomalies 367

    (patterns 3 and 4) after the mid 1970s, particularly from the mid 1990s to the present. These 368

    frequency trends have contributed to tropical Pacific warming, particularly in the western Pacific 369

    and eastern equatorial Pacific regions (Fig. 6a). One may hypothesize that this behavior reflects 370

    a long-term warming trend most pronounced in the western Pacific warm pool superimposed on 371

    interannual ENSO variability. However, this analysis suggests that there is a disproportionate 372

    western Pacific warming for La Nia-like patterns, while there is no similar trend in the western 373

    Pacific evident for the El Nio-like patterns3. In fact, the positive trend in the frequency of El 374

    Nio-like patterns, particularly pattern 8, contributes to a weak negative SST trend in the west 375

    Pacific warm pool region (Fig. 6b). Therefore, this analysis suggests that the simple paradigm of 376

    a long-term trend superimposed on interannual variability, as typically assumed in global 377

    warming attribution studies (e.g., Pall et al. 2011), may not be sufficient for understanding 378

    tropical Pacific SST variability and trends. Rather, changes in the frequency distribution of 379

    interannually varying patterns within the ENSO continuum, as depicted in Fig. 2, may impart a 380

    significant contribution to the long-term trend. Moreover, recent theoretical work (Liang et al. 381

    2012) proposes that the recent elevation in ENSO variance may be more of a cause than a 382

    3 See Fig. 10 of LHeureux et al. (2012) for additional evidence of enhanced west Pacific warm pool warming trends

    in La Nia episodes relative to El Nio episodes during November February.

  • 18

    consequence of eastern tropical Pacific warming, which would further underscore the difficulty 383

    of separating interannual variability from the tropical mean state. 384

    The trend toward La Nia-like patterns with positive SST anomalies in the western 385

    Pacific warm pool is of particular interest because this general pattern may represent the perfect 386

    ocean for drought over many midlatitude regions (Hoerling and Kumar 2003). This SST 387

    pattern, captured by SOM patterns 3 and 4, dominated during the period between 1998 and 2002 388

    (Fig. 3), which was a period of prolonged drought throughout much of the United States, 389

    southern Europe, and Southwest Asia. Climate model simulations suggest that both the negative 390

    SST anomalies in the eastern Pacific and positive SST anomalies in the western tropical Pacific 391

    acted synergistically to force the persistent drought during this period (Hoerling and Kumar 392

    2003; Lau et al. 2006). Figure 3 reveals that SOM patterns 3 and 4 occurred several additional 393

    times since that period. In addition, there is evidence that the positive trend in Indo-Pacific 394

    warm pool SSTs has contributed to changes in the wintertime teleconnection response to La 395

    Nia, a trend toward a more zonally oriented circumglobal teleconnection pattern (Kumar et al. 396

    2010; Lee et al. 2011). Given the widespread societal impacts of these particular La Nia 397

    flavors, it is worthwhile for future studies to investigate whether the disproportionate warm pool 398

    warming for La Nia-like patterns shall continue. 399

    Both an EP (pattern 9) and CP/EP El Nio (pattern 8) SOM pattern also have experienced 400

    positive trends in the frequency of occurrence over the past 60 years, but these trends are 401

    indistinguishable from natural variability (Fig. 4). Given the recent focus on whether CP El 402

    Nio episodes will become more frequent under global warming (Yeh et al. 2009), the positive 403

    trend of CP El Nio-like SOM pattern 8 is of particular interest. However, the lack of a 404

    significant trend is consistent with recent studies based on long integrations of a multivariate red 405

  • 19

    noise model (Newman et al. 2011b) and a coupled climate model (Yeh et al. 2011), which found 406

    that the recent multidecadal increase in CP El Nio relative to EP El Nio episodes is consistent 407

    with natural variability. 408

    The changes in frequency of the ENSO flavor SOM patterns have contributed to an 409

    overall positive SST trend in the central and eastern equatorial Pacific region (Fig. 5b), which is 410

    consistent with recent findings linking positive equatorial Pacific trends to ENSO (Compo and 411

    Sardeshmukh 2010; Lee and McPhaden 2010; LHeureux et al. 2012). In addition, the increased 412

    dominance of SOM patterns 3 and 4 at the expense of patterns 1 and 2 has contributed to the 413

    warming trend in the tropical West Pacific region. The residual SST trend (Fig. 5c) reveals 414

    positive SST trends in the western Pacific but weak or even negative SST trends throughout the 415

    equatorial eastern Pacific region. Interestingly, this residual trend in Fig. 5c is somewhat similar 416

    to the ENSO-unrelated SST trends obtained after applying a dynamic ENSO filter (Compo and 417

    Sardeshmukh 2010; Solomon and Newman 2012). This particular filter, which accounts for the 418

    SST evolution during ENSO and is obtained through a linear inverse modeling approach, reveals 419

    a trend pattern of western Indo-Pacific warming and eastern equatorial Pacific cooling after the 420

    trends associated with ENSO have been removed. The approach adopted here similarly shows 421

    that ENSO-related trends have contributed to eastern equatorial Pacific warming (Fig. 5b), and 422

    the residual SST warming is most pronounced in the west Pacific warm pool (Fig. 5c). 423

    However, we must exercise caution when viewing long-term SST trends, given the data 424

    uncertainties. In particular, a recent SST reconstruction based only on bucket SST and nighttime 425

    marine surface air temperature measurements suggests less pronounced western Pacific warming 426

    relative to that of the eastern Pacific (Tokinaga et al. 2012). Although beyond the scope of this 427

    study, future research shall continue to investigate whether this enhanced western Pacific 428

  • 20

    warming is real, and, if so, whether it represents a response to anthropogenic warming (Clement 429

    et al. 1996, Cane et al. 1997) or if enhanced equatorial Pacific warming, as in global climate 430

    models (Collins et al. 2010; Xie et al. 2010), is more likely. The interplay between the potential 431

    impact of greenhouse gas warming on ENSO (Guilyardi et al. 2009; Yeh et al. 2009; Collins et 432

    al. 2010; Vecchi and Wittenberg 2010) and on long-term SST trends is a challenging problem, 433

    but the approach presented here provides a possible framework for exploring this interaction. 434

    435

    5. Conclusions 436

    This study opens with the question: how many ENSO flavors can we distinguish? To 437

    address this question, we examine an approach that partitions tropical Pacific SST fields through 438

    SOM analysis and then determines the maximum number of SOM cluster patterns that are 439

    statistically distinguishable. This approach can be applied more generally to other cluster 440

    analysis problems, particularly those of K-means cluster or SOM analysis, in order to answer the 441

    recurring question of what is the optimal, or at least the maximum number of clusters to retain. 442

    The approach adopted here has the appeal of being grounded in an accessible concept, statistical 443

    distinguishability. Many other applications with serially correlated data would face the 444

    additional challenge of accounting for serial correlation in the calculation of local p-values, but 445

    the basic approach described here still would apply. 446

    Although the present study focuses on seasonal SST patterns, ENSO also undergoes other 447

    types of interdecadal variations, including changes in the seasonal evolution of ENSO-related 448

    SST anomalies. Future extensions of this study may explore seasonal variations of ENSO 449

    flavors. In addition, the dynamical processes responsible for these nine patterns remain an open 450

    question. Through a multivariate red noise framework for tropical SST variability, Newman et 451

  • 21

    al. (2011a,b) find that the leading optimal structure corresponding with the EP ENSO is driven 452

    by both surface and thermocline interactions, as in the classic recharge-discharge mechanism 453

    (Jin 1997). In contrast, the optimal structure corresponding with CP ENSO evolves through non-454

    local SST interactions, such as the advection of SST anomalies, but without the recharge-455

    discharge mechanism. The CP ENSO event growth is more modest than that of the EP ENSO, 456

    but the lack of a discharge mechanism allows the CP ENSO to decay more slowly (Newman et 457

    al. 2011b). Because these two optimal initial structures are orthogonal, the framework of 458

    Newman et al. (2011a,b) suggests a continuum of mixed CP/EP ENSO patterns with 459

    intermediate dynamical characteristics. The analysis presented here is consistent with this 460

    general framework, but additional work is needed. 461

    The analysis presented here also suggests that although El Nio flavors often receive 462

    more focus than those of La Nia in the literature, changes related to La Nia-like SST patterns 463

    have made a stronger impact on long-term SST trends over the past 60 years. A number of 464

    outstanding questions remain. Given that tropical Pacific SST anomalies have far-reaching 465

    effects through tropical convection anomalies and the triggering of atmospheric teleconnections, 466

    future research shall augment recent efforts (e.g., Larkin and Harrison 2005; Weng et al. 2007; 467

    Mo 2010; Hu et al. 2012) to examine how many ENSO flavor teleconnections and remote 468

    impacts can be distinguished. In addition, the various ENSO flavors within the ENSO 469

    continuum and their relationship with the long-term SST trend remain an active area of research 470

    (Guilyardi et al. 2009; Yeh et al. 2009; Collins et al. 2010; Liang et al. 2012). A unique set of 471

    questions raised in this study relates to the trend toward La Nia-like patterns with enhanced 472

    SST anomalies in the west Pacific warm pool. Why has there been disproportionate west Pacific 473

    warming for La Nia patterns? Will this trend continue? Can coupled global climate models 474

  • 22

    capture this sort of variability? The approach presented here provides a framework for 475

    examining the ENSO continuum and questions like these with a manageable set of representative 476

    ENSO flavors. 477

    478

    Acknowledgments. 479

    I sincerely thank Drs. Steven Feldstein, Sukyoung Lee, Jinbao Li, and Shang-Ping Xie for 480

    thoughtful discussions and helpful comments that contributed to this work. I also thank Dr. Eli 481

    Tziperman and two anonymous reviewers for constructive comments that improved the quality 482

    of this study. I am grateful for support through a grant from the NOAA Climate Test Bed 483

    program. NOAA ERSST V3 data are provided by the NOAA/OAR/ESRL PSD, Boulder, 484

    Colorado, USA, from their Web site at http://www.esrl.noaa.gov/psd. 485

    486

    487

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  • 32

    List of Figures 705

    FIG. 1. The number of SOM SST cluster pattern pairs that are statistically indistinguishable at the 706

    95% confidence level as a function of the number of SOM patterns, K. 707

    708

    FIG. 2. The nine SST anomaly cluster patterns for a one-dimensional SOM. The contour interval 709

    is 0.2C, with the zero contour omitted. Stippling indicates anomalies that are statistically 710

    significant above the 95% confidence level. The percentages to the bottom right of each map 711

    refer to the frequency of occurrence of the pattern for the 1950-2011 period. 712

    713

    FIG. 3. Occurrence time series for each of the nine SOM patterns in Figure 2 (the assigned year 714

    corresponds to that of January-February in the September-February season). Filled bars indicate 715

    pattern occurrence for the particular year. Red (blue) bars indicate the occurrence of an El Nio 716

    (La Nia) episode during at least four of the six months, and grey bars indicate the classification 717

    as an ENSO neutral season. 718

    719

    FIG. 4. Trends in the frequency of occurrence for each of nine SOM patterns in Figure 2. Filled 720

    bars signify trends that are statistically significant above the 95% confidence level with respect 721

    to a nine-state first order Markov chain (see text for details). 722

    723

    FIG. 5. (a) Total and (b) SOM-derived September February SST trend (C/50 years) for 1950-724

    2011. (c) Difference between total and SOM-derived SST trends [(a) minus (b)]. The contour 725

    interval is 0.1C/50 years, and the zero contour line is omitted. 726

    727

  • 33

    FIG. 6. As in Fig. 5b but calculated only for (a) La Nia-like SOM patterns 1-5 and for (b) El 728

    Nio-like SOM patterns 6-9. 729

    730

    731

    732

    733

    734

    735

    736

    737

    738

    739

    740

  • 34

    FIG. 1. The number of SOM SST cluster pattern pairs that are statistically indistinguishable at the

    95% confidence level as a function of the number of SOM patterns, K.

  • 35

    FIG. 2. The nine SST anomaly cluster patterns for a one-dimensional SOM. The contour interval

    is 0.2C, with the zero contour line omitted. Stippling indicates anomalies that are statistically

    significant above the 95% confidence level. The percentages to the bottom right of each map

    refer to the frequency of occurrence of the pattern for the 1950-2011 period.

  • 36

    FIG. 3. Occurrence time series for each of the nine SOM patterns in Figure 2 (the assigned year

    corresponds to that of January-February in the September-February season). Filled bars indicate

    pattern occurrence for the particular year. Red (blue) bars indicate the occurrence of an El Nio

    (La Nia) episode during at least four of the six months, and grey bars indicate the classification

    as an ENSO neutral season.

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    FIG. 4. Trends in the frequency of occurrence for each of nine SOM patterns in Figure 2. Filled

    bars signify trends that are statistically significant above the 95% confidence level with respect

    to a nine-state first-order Markov chain (see text for details).

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    FIG. 5. (a) Total and (b) SOM-derived September February SST trend (C/50 years) for 1950-

    2011. (c) Difference between total and SOM-derived SST trends [(a) minus (b)]. The contour

    interval is 0.1C/50 years, and the zero contour line is omitted.

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    FIG. 6. As in Fig. 5b but calculated only for (a) La Nia-like SOM patterns 1-5 and for (b) El

    Nio-like SOM patterns 6-9.

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